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What does fundamental (homotopy) groups measure?

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#algebraic-topology #fundamental-groups #higher-homotopy-groups
611
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Whitehead product and a homotopy group of a wedge sum

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#algebraic-topology #homotopy-theory #cw-complexes #higher-homotopy-groups
99
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Quotient map for the two formulations of relative homotopy groups

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#general-topology #algebraic-topology #homotopy-theory #quotient-spaces #higher-homotopy-groups
76
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Reference requested for homotopy theory theorem

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#reference-request #differential-topology #smooth-manifolds #homotopy-theory #higher-homotopy-groups
443
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How torsion arise in homotopy groups of spheres?

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#algebraic-topology #homotopy-theory #covering-spaces #cw-complexes #higher-homotopy-groups
81
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Reference for first appearance of Samelson product

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#homotopy-theory #loop-spaces #higher-homotopy-groups
148
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Isomorphism between homotopy groups of CW-complexes

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#algebraic-topology #homotopy-theory #cw-complexes #higher-homotopy-groups
210
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Is the splitting $\pi_{k}(X,A)\simeq\pi_{k}(X)\times \pi_{k-1}(A)$ a $\pi_1(A)$-modules isomorphism?

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
285
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Action of $\pi_1(G)$ on $\pi_n(G)$ is trivial for a topological group $G$, i.e. $G$ is a n-simple space.

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#algebraic-topology #homotopy-theory #topological-groups #fundamental-groups #higher-homotopy-groups
71
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Show that $(f+g)_{\ast}=f_{\ast}+g_{\ast}$

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#general-topology #algebraic-topology #homology-cohomology #higher-homotopy-groups
274
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Prove that $S^n$ is $(n-1)$-connected.

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#algebraic-topology #higher-homotopy-groups
219
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Calculating higher homotopy groups of (complements of) knots

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#reference-request #algebraic-topology #knot-theory #higher-homotopy-groups
142
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A confusion on $\Omega$ and $\Sigma$ functors

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
201
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How to show that higher Hopf fibrations are not nullhomotopic?

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#algebraic-topology #homotopy-theory #higher-homotopy-groups #hopf-fibration
273
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Defining higher homotopy in terms of embeddings $S^n \hookrightarrow X$?

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#algebraic-topology #homotopy-theory #higher-homotopy-groups

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